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ATTORNEK United States Patent 3,148,317 TUGL RADIUS CGRRECTIGN CGMPUTERRobert W. Tripp, Bronxvilie, N.Y., assignor, by mesne assignments, toInductosyn Corporation, Carson City, Nev., a corporation of Nevada FiledSept. 6, 1956, der. No. 6%,357 20 Claims. (Cl. 318-28) This inventionrelates to two or three dimensional tool radius correction computers andmore particularly to the control of machine tools in which the rotatingcutter of finite radius and a workpiece are moved relatively to eachother according to a program of two or three dimensional informationsupplied to the traversing drives of the workpiece carriage or cuttinghead in the machine tool in order to generate on the workpiece a surfaceor profile of specified shape.

Patent 2,843,811, issued July 15, 1958, in applicants name, disclosesand claims a three dimensional machine control servosystem. This systemprovides a continuous machining operation, a data input device supplyingsignals representing selected coordinates along the curve to be out. Acomputer accepts the input data and converts it into rate drive commandsfor the machine drives. The machine parts move along their separate axessimultaneously at continuously changing rates and the required curve iscut in the workpiece. The system is an analog type of system and itoperates with great accuracy, particularly as the instructionstransmitted to and received by the machine drives are in a plurality ofgrades of increments, one of which is a fine grade for which the highlyaccurate Inductosyn (Pat. No. 2,799,835) is provided.

The present application is a continuation-in-part of copendingapplication S.N. 561,769, filed January 27, 1956, for Tool RadiusCorrection Computer System, now abandoned. The present inventionincludes a tool radius computer which provides a basic or recordedprogram in terms of the two dimensional contour of the desired workpieceto the exclusion of a correction for the tool radius, with a separatetool radius control. This avoids the very laborious digital computationrequired according to prior practice, if the cutter radius is changed,for the reason that while the basic or recorded program heretofore tookinto account a correction for the tool radius, it did so by making anallowance for the tool radius an integral part of the basic program,requiring that such basic program be changed if the tool radius ischanged.

The present invention also includes a two dimensional tool radiuscomputer which programs and deals with signals representing the angle 0between the tool path in the X, Y plane and the X axis.

According to the present invention, the basic, i.e., the recordedprogram is in terms of both the two and three dimensional contour of thedesired part to the exclusion of a correction for the tool radius. Thisbasic program is then converted by an analog computer provided by theinvention, into a program of cutter center locations for the machinetool, the cutter radius being inserted separately, either manually orautomatically into the computer. The computer thus derives from theprogram of the desired surface the corrections to that program necessaryto provide the machine tool with a program of cutter center locationsfor it to follow.

The invention greatly reduces the amount of digital computation whichmust be performed in the initial programming of the part to be cutdespite the necessity thereby involved, as will be presently explained,of programming not only the desired finished surface but also the angle0 between the tool path component in X, Y plane and the X axis, and theangle that the tool path extends 1 Trademark.

out of that plane, in terms of the program for the desired finishedsurface.

As in SN. 561,769, now abandoned, another important advantage of theinvention is the facility with which the cutter size may be changed,without recomputation of the basic program. A change from positive tonegative in the cutter radius input to the computer results in transferof the cutter motion from one to the opposite sides of the profilespecified by the basic program information. In this way matching maleand female parts can be cut from the same program. By using in thecomputer a cutter radius setting slightly different from that of thecutter actually employed, the machine tool can be caused to cut theworkpiece a corresponding amount larger or smaller than is called for bythe program of the workpiece itself. Thus mating parts can be cut with apredetermined space between them, as is useful in the production ofstamping dies. Roughing cuts can also be made by this method, followedby a finishing cut made with a different sized cutter or with the samecutter upon proper adjustment of the cutter radius setting in thecomputer of the invention.

For further details of the invention, reference may be made to thedrawings wherein FIG. 1 is a schematic diagram of various kinds of inputdata characteristic of a tool path, and feed rate input data, for adigital-to-analog converter for converting such data to analog values ofthe angle 0 representing the angle of the component of the tool path inthe X, Y plane as indicated in FIG. 10.

FIG. 2 is a similar schematic diagram of input data characteristic ofthe tool path and a digital-to-analog converter providing analog valuesof the angle representing the angle of the tool path above the X, Yplane, that is in a plane containing the tool path and the Z axis atright angles to the X, Y plane.

FIG. 3 is a schematic diagram showing schematically in perspective acomponent solver having inputs of 6 and 0+ and having outputs of sin 0cos 4) and cos 0 cos 4 with integrators for integrating the feed ratewith such components.

FIG. 4 schematically illustrates a resolver having an input 5 and a feedrate integrator therefor.

FIG. 5 schematically illustrates a shaft input of 0 from FIG. 1 with atool radius resolver for obtaining the tool radius correction incrementsAx and Ay, the resolvers in FIG. 5 also having an input from FIG. 6which schematically shows a tool radius computer for computing the toolradius correction increment Az, and having a shaft input of angle fromFIG. 2 and also an input of tool radius R.

FIG. 7 schematically illustrates the machine or driven elements on the Xand Y axes, as controlled in coarse, medium and fine increments of X andY shaft inputs from FIG. 3 and as modified by the coarse, medium andfine increments of the tool radius corrections Ax and Ay.

FIG. 8 corresponds to FIG. 7 in showing a similar coarse, medium andfine control of the machine or driven elements for the Z axis asdetermined by the Z shaft input from FIG. 4 as modified by the toolradius correction Az from FIG. 6.

FIG. 9 is a schematic diagram illustrating the radius FIG. 13 is a planview of a machine tool having drives 3: along X, Y and Z axes foradvancing a workpiece and a cutter or tool relatively to each other.

While the drawings and description deal specifically with 3D operation,the system shown and described is useful for 2D operation, being zero,so that sin is zero and cos is one. For 2D operation, the sine andcosine of are integrated with the feed rate.

Referring in detail to the drawings, as shown in FIG. 10, the tool path1 is illustrated with reference to the three dimensional coordinate axesX, Y and Z, the angle 0 representing the angle between the X axis andthe tool path component 2 in the X, Y plane while the angle representsthe angle that the tool path 1 is or extends above or out of the X, Yplane. As disclosed and claimed in SN. 608,024, now Patent 2,843,811,July 15, 1958, means are provided for supplying analog values of 0 and gand for resolving these angles into their components X, Y and Zaccording to the following formulae, the tool path being considered asunity.

X =cos 0 cos Y=sin 0 cos Z=sin p The term sin or Z is solved with theresolver R1 in FIGS. 4 and 12, while the terms cos 0 cos and sin 0 cosare solved by the component solver R2 in FIGS. 3 and 12. As shown inFIG. 12, the component solver R2 has as inputs the value 0 and also thevalue .0+ obtained from the adder 3 which has both 0 and qb as inputs.Referring particularly to Patent 2,843,811, the component solver for Xand Y is indicated at R2 in FIG. 9 and shown in detail in FIG. 3, theadder for the angles 0 and is shown at 3 in FIG. 9 and in detail in FIG.3, while the component solver for Z is indicated at R1 in FIG. 9 andshown in detail in FIG. 4; see also the general description of theseelements appearing under the heading 2. Resolving Unit, page 7, line 19to page 8, line 10.

By integrating the feed rate with values proportional to the componentsabove described and shown in FIG. 10, the tool or other driven elementis caused to follow a path in space in accordance with digital inputdata from FIGS. 1 and 2 appropriate to those angles. The X and Y machinedrives are indicated in FIG. 7 while the Z machine drive is indicated inFIG. 8, as will be described in detail later.

FIG. 9 illustrates the tool radius corrections, Ax, Ay and Az involvedin applying the invention to the cutting of compoundly curved(non-cylindrical) surfaces by means of a spherical cutter. In FIG. 9, 1'represents the periphery of a spherical cutter with center at 2. 3'represents the surface of the workpiece '7 to be machined tangent to thecutter at 9. The radius of the cutter, drawn normal to the surface 3 isindicated at R, which extends at an angle as to the plane defined by apair of two dimensional coordinate axes X, Y to which a third coordinateaxis Z is perpendicular. The projection of R in the X, Y plane is R,which is inclined at an angle 6 to the X axis. The radius R to becorrected for is thus broken down into three components Ax, Ay and AZ.As shown in FIG. 12, such correction may be achieved by means of theresolvers in FIGS. 6 and 5, these resolvers being connected in tandem asshown in FIG. 12. The inputs to the resolver of FIG. 6 are R and theoutputs being Az and R. The inputs to the resolver of FIG. 5 are 0 andR, and its outputs are Ax and Ay. By addition of the corrections Ax, Ayand Az to the respective X, Y, and Z coordinates of the workpieceprogram, the cutter center can be correctly positioned to hold thecutter surface tangent to the desired workpiece surface. The correctionAx is R cos 0 cos 5, see column 14, line 70. The correction Ay isR sin 0cos ,see column 15, line 9. The correction Az is R sin gb, see column15, line 24. The programmed data on the workpiece include the values ofX, Y, Z and the angles and 6.

Before proceeding with a detailed description, reference may be made toFIG. 12 which illustrates schemati- All.

cally the manner in which the angular components 0 and p are obtainedand also how they are employed for bringing about the three dimensionalcontrol of the machine tool with correction for the radius of the tool.The tool radius itself is a separate and adjustable input and isrepresented at R in FIG. 12 as an input to the block 1110 markedResolver FIG. 6. Block 111 represents the input and digital-to-analogconverter of FIG. 1, having a shaft output carrying the instruction ofthe angle 0. The block 112 represents the input and digital-to-analogconverter of FIG. 2 having a shaft output carrying the instruction ofangle The shaft instruction of 0 and the shaft instruction of 4, areadded as indicated in adder 3 of FIG. 12, see also FIG. 3, and thevalues 0 and 0+ are combined in the resolver R2 thus marked in FIGS. 3and 12, providing the components cos 0 cos 11 and sin 0 cos qb, whilethe output from block 112 is resolved in resolver R1, thus marked inFIGS. 4 and 12, to provide the component sin b. The feed rate FRindicated in FIG. 12 is integrated with each of the three commandcomponents above mentioned by integrators 13 and 14 as shown in FIGS. 3and 12 to provide the X and Y shaft rotations of the feed rates, thefeed rate also being integrated by the third component as indicated byintegrator 15 in FIGS. 4 and 12 to provide a shaft rotation of the Zcomponent of the feed rate. As above explained, the tool radiuscorrections, as indicated at the bottom of FIG. 12 are derived from theresolvers in FIGS. 6 and 5. The tool radius corrections Ax, Ay and Azare electrical in nature and they are added to the respectiveX, Y and Zshaft rotations by means of resolvers in FIGS. 7 and 8 to provide theoutputs X-l-Ax, Y-l-Ay and Z +Az. In fact, the invention provides the X,Y and Z shaft instructions in coarse, medium and fine increments andalso provides the electrical tool radius corrections Ax, Ay and Az incoarse, medium and fine increments, for servoing the X, Y and Z machineelements indicated in FIGS. 7 and 8.

The X, Y and Z lead screws or machine elements of FIGS. 7 and 8represent the conventional coordinate drives of a machine tool. Theconstruction of the machine tool and its arrangement for advancing thecutter with respect to the workpiece may be as shown in FIG. 13, or thespindle which supports the cutter may be fixed and the workpieceadvanced with respect to it. The diagrammatic showing of FIG. 13illustrates how orthogonal drives may be provided for advancing aworkpiece with respect to a rotating cutter to form on the workpiece acontour which may be defined in advance as a function of rectangularcoordinates whose axes are parallel respectively to the perpendiculardirections of relative cutter-workpiece motion provided by such drives.

In FIG. 13, the bed 231 of a machine tool has removably fixed thereto aworkpiece 232 for engagement with a cutter 224. Ways 230 on the bedsupport a carriage 229, coupled at nut 194 to lead screw 210 which isjournaled in the bed, and driven by motor 189. Carriage 229 itself isprovided with ways 228 perpendicular to ways 230, and a carriage 227riding on ways 228 is coupled by nut 195 to lead screw 221, journaled incarriage 227 and driven by motor 1%. The cutter 224 is spindled in ahead 225 attached to carriage 226 with its axis and with ways or slide223 and lead screw 179 perpendicular to the plane of motion of cmriage227. X, Y and Z coordinate axes are shown on the bed 231 parallel to theways 230, 228, and 223 respectively. The following additional generaldescription may also be considered as it includes a further explanationof the relation between the present application, the corresponding twodimensional case SN. 557,035, Patent 2,875,390, February 24, 1959, andthe three dimensional case Patent 2,843,811.

Patent 2,875,390 describes and claims three basic parts, disclosedherein, as follows:

(1) The command unit of FIG. 1 which determines continuously varyingvalues of angle 0 atshaft 4 from decimal, digital inputs D3 of slope, D4of curvature, D5 of rate of change of curvature and D2 of feed rate;referring to Patent 2,875,390, the corresponding input is shown at D1 toD4 in FIG. 1 and the corresponding shaft is shown at 8 in FIGS. 16 and17.

(2) The resolving unit which operates on the values of angle 0 andvalues of the feed rate to determine the X and Y coordinates in terms ofthe angular position of the shaft corresponding to shaft 4 in FIG. 1;referring to Patent 2,875,390, the corresponding resolver is shown at R3in FIG. 17.

(3) The driving unit similar to present FIG. 7, which converts the X andY shaft instructions to coarse, medium and fine electrical signals whichin turn cause the machine elements to servo to the correct positions;referring to Patent 2,875,390, the corresponding driving unit is shownin FIG. 18, having coarse, medium and fine data elements at 322, 329 and382 respectively, for axis X and similar data elements for axis Y.

Generally speaking, the two dimensional case has been extended to threedimensions as disclosed and claimed in Patent 2,843,811, by making thefollowing improvements:

(1) Command Unit. The command unit includes not only the command unit ofFIG. 1 as described above for obtaining continuously varying values ofangle 0 at shaft 4, but it also includes, as shown in FIG. 2, decimaldigital values and inputs D6 of slope, D7 of curvature and D8 of rate ofcurvature change and digital-to-analog converters controlled thereby forobtaining continuously varying values of angle p at shaft 5. The shaftinstruction of angle p is an input to the resolver of present FIG. 6,and the latter supplies an input to the resolver of FIG. 5, to provide aseparate control for the tool radius on a three dimensional basis,according to the present invention.

(2) Resolving Unit. As above described in connection with FIG. 10,taking the tool path as unity, its component Z=sin qb is obtained with aconventional resolver R1 in FIGS. 4 and 12, while its other components X=cos 0 cos and Y=sin 0 cos qb are obtained with the resolver R2 in FIGS.3 and 12. The resolver R2 is an improved component solver described andclaimed in Patent 2,843,811, and while a detailed description of thismechanism will be given later, at this point it may be noted that thisresolver R2 is a combination of three devices, namely:

(a) A sine-cosine mechanism.

(b) A planetary dilferential, in that the outer frame 6 is driven aboutits axis at angle 0 (by pinion 7 which drives gear 8 on frame 6) frame 6having a ring gear 9 having inwardly extending teeth 10 which mesh withthe teeth 11 on planetary gear 12 which rotates about its axis andhaving a rotary support 130 at the outer end of a crank 114, the innerend of crank 114 being fixed to shaft 115 which rotates on the axis offrame 6 at angle 0+. The sum of 0 and p is the output of adder 3 inFIGS. 3 and 12, FIG. 3 showing this adder as a differential gear unithaving inputs of 0 from shaft 4 in FIG. 1 and from shaft 5 in FIG. 2,via FIG. 4.

(c) A resolver, in that the sliders 16 and 17 have slots 18 and 19 of aScotch yoke mechanism 20 applied to the crank pin 21 on gear 12 whichrotates inside of ring gear 9.

(3) Driving Unit. In addition to the drives for the X and Y machineelements as in FIG. 7, the invention adds a drive for the Z machineelement as in FIG. 8, wherein the null for the servo system of motor 181is displaced by the differential synchro transmitter 133 in accordancewith the Z component of the tool radius control on line 129 from FIG. 6.Y

The invention will be described in further detail under the followingheadings, which represent various components of the machine controlmethod and system; feed rate, the command unit of FIG. 1, command unitof FIG. 2, component solver of FIG. 3, resolver of FIG. 4,

6 tool radius computer of FIGS. 5 and 6, the X and Y driving units ofFIG. 7, the Z driving unit of FIG. 8, program advance and supervisorycontrol of feed rate, and general operation.

Feed Rate In FIG. 1, the input D2 supplies a decimal digital input offeed rate to the analog feed converter 24 which sup plies a voltage asdisclosed in Patent 2,875,390 for comparison with the voltage oftachometer 25 driven by feed rate motor M1; referring to Patent2,875,390, see FIGS. 2 and 13, and page 38, lines 18 to 26. The servoindicated at 26 drives the motor M1 at such a rate that the diflierencebetween the voltage generated by the stepping switch conversion circuit,not shown, of the converter 24 and the tachometer 25 is essentiallyzero.

The feed rate motor M1 drives the feed rate shaft FR which in FIG. 1 isalso an input indicated at FR3 to the variable gear ratio VGI, describedlater and also an input indicated at FR4- to the ball-disk-cylinderintegrator BDCI, described later.

As shown in FIG. 3, the feed rate FR is also an input indicated at FR40to the ball-disk-cylinder integrator 13, and an input FRS to theball-disk-cylinder integrator 14, these integrators, as later described,being controlled by the sliders 16 and 1'7 of resolver R2, pertaining tothe X and Y machine elements.

As shown in FIG. 4, the feed rate FR is an input PR6 to theball-disk-cylinder integrator 15 in the output of resolver R1 andpertaining to the Z machine element.

As shown in FIG. 2, the feed rate FR is also an input PR7 to thevariable gear ratio VG2 and an input FR8 to the ball-disk-cylinderintegrator 22 later described.

Command Unit 0 FIG. 1

In FIG. 1, the slope data D3 represents a decimal numher in terms ofangles, the curvature data D4 represents a decimal number in terms ofthe reciprocal of radius and the rate of curvature change data D5represents a number in terms of speed, the speed number, as describedand claimed in Patent 2,875,390 being in a system of numeration having aradix of 2 to the Nth power, where N is an integer here shown as 3, thesystem being octal; referring to Patent 2,875,390, see the descriptionunder the heading (a) Octal-to-binary translator.

The slope 0 of the component 2 in the X, Y plane of the tool path 1, seeFIG. 10, depends upon the ratio of the feed rates of the corresponding Xand Y machine elements of FIG. 7. This ratio is established with asingle datum of input information D3. This is accomplished bypositioning the shaft 4 in FIG. 1 in accordance with the slope data D3and by resolving the angular position of the feed rate resolver R2 inFIG. 3 into co-function controls in space quadrature, by operating theball slides 27 and 28 of resolver R2 as inputs for the integrators 13and 14 to establish the feed rates at shafts S11 and S12, FIG. 3, toestablish the feed rate ratio on the X and Y axes.

The resolver shaft position 0 is established from input information D3of slope angles expressed in terms of angles on a decimal basis, adital-to-analog converter 44 being provided to convert this input to theangular position 0 of shaft 4 as described and claimed in co-pendingapplication S.N. 540,748, filed October 17, 1955, by R. W. Tripp, forAutomatic Shaft Control, Patent 2,839,711, June 17, 1958, and assignedto the assignee of the present application, referring to Patent2,839,711, the shaft 8 in FIG. 7 is positioned by the angle data 1 inFIG. 1, that application also disclosing and claiming a computer forcomputing the sine and cosine values of an angle equal to the sum of theangles represented by the digits in decimally related digital groups asindicated by the input D3, the position of shaft 8 in FIG. 7 of Patent2,839,711, being controlled by the cosine and sine coils 34, 35 of thecoarse data element 37 and by coils and 131 of the s fine data element68, the converter including the 100 and 10 step computers of FIG. 1, thedecimal to noval converter of FIGS. 1 and 2, the 1, step computer ofFIG. 5, the .l step computer of FIG. 3, the quadrant converter of FIG. 6and the accompanying description. Said applications also disclose andclaim producing the co-function sine and cosine values of the angle incoarse and fine increments, the coarse increment being supplied to thecoarse resolver 29, the fine increment to the Inductosyn 3d. Forexample, the coarse increment of sine may be supplied to winding 31, thecoarse increment of cos 0 to winding 32, windings 31 and 32 being inspace quadrature and inductively related to the relatively rotatablewinding 33 having a driving connection as indicated at 34 to therelatively rotatable winding 35 of Inductosyn 30. The fine increment ofsin 6 may be supplied to winding 36, the fine increment of cos 0 t0winding 37. Windings 36 and 37 are inductively related to the relativelyrotatable winding 35, the latter having a driving connection indicatedat 38 to gear 39 of differential gear DG1. Gear 39 is connected by gear419 to servo'motor 41 having an amplifier 42 and controlled by a wellknown synchro switch 43. Motor 41 provides a shaft input to thedifferential gear D61 and operates it to thereby operate resolver 29 andInductosyn Ed, in turn to reduce to zero the error current in windings33 and 35, whereby shaft 4 is driven to an angular position or tocontinuously varying positions in accordance with the data D3.

Patent 2,849,668 describes and claims a decimal input in terms of alinear dimension and computes the sum of angles corresponding to thelinear input for supply to data elements in a servosystern, the linearinput 4- of FIG. 4 and applying also to FIGS. to 9 as indicated,operating the computer of those figures to operate the coarse, mediumand line data elements 1, 2 and 3 of FIG. 10.

Application SN. 540,429 is now Patent 2,849,668, August 26, 1958.

The circuit of motor d1 is controlled by a switch S3 9 later described.

As described and claimed in the above mentioned patent applications, theratio of the speed rates of the driven elements on the X and Y axes ischanged, as required for a circular path, i.e., part or all of a circle,with a single datum of curvature input information D4. The input D4 thusprovides curvature input information on a decimal basis in terms ofcurvature (reciprocal of radius) and the converter converts this digitaldata to an analog value expressed as a shaft speed for addition to theposition of shaft 4 as determined by the slope control D3.

As described and claimed in Patent 2,875,390, the differential gear DGZhas a spider having an output shaft S5 driven at a speed equal to thesum of the speed of shaft S3 from the rate of curvature change and thespeed of shaft S2 driven by servo motor M2; referring to Patent2,875,390, to differential gear DQ4- in FIG. 15 and description page 31,lines 11 to 26. The shaft S5 is a part of the spider and it has adriving connection 46 with the slider 47 of a potentiometer 4-8, theservo circuit including motor M2 and amplifier 49 driving the shaft 52and hence gears 5d and 511 and gear "52 to a position or at a speedwhich reduces to zero the error current determined by the differencebetween the potentials established by the position of slider 47 and thecurvature instruction from converter 45, as setup in the input D4.

Switch Sid is similar in function to switch S35 to render its servomotor M2 inactive at certain times as described later.

The shaft S5 thus in part at least is driven to a position or at a ratedependent upon the curvature instruction in the input D4. Shaft S5operates gear 53 which operates the ball slide M to integrate the feedrate drive PR4 accordingly, the output shaft S1 being added throughgears 55 and 56 to the shaft 4 through the differential gear D61.

As described and claimed in Patent 2,875,390, the rate of change ofcurvature input data D5 is converted into analog form to provide aposition or continuously varying speed values of shaft S3 which is addedthrough differential gear DGZ to the position or speed of shaft S5,whereby the curvature instruction in shaft S5 is thus modified inaccordance with the rate of curvature change instruction in the inputD5.

Hence the 0 shaft 4 in FIG. 1 is controlled by the combined eflfect ofthe instructions in all of the inputs D3, D4 and D5, whereby thecombined effect of all of these instructions may be resolved intoco-function space quadrature feed rates for the X and Y drives.

Command Unit of FIG. 2

Referring to FIG. 2, the circuit here shown is similar to the circuit inFIG. 1, the slope input D6, the curvature input D7 and the rate ofcurvature change D8 corresponding to the inputs D3, D4 and D5respectively. The circuits and devices controlled by the inputs D6, D7and D8 are also similar to the corresponding items in FIG. 1, with thismain difference, that the inputs D6, D7 and D8 have values appropriateto positioning or driving the shaft 5 at the angle ((1, appropriate tothe Z machine element, see FIGS. 8, 12.

Accordingly, the slope data in the input D6 is converted by converter 69into coarse and fine increments of sine and cosine values by the coarseresolver 61 and the Inductosyn 62 which are driven by the servo motor63, under control of synchro switch 64, to reduce the error current tozero, as previously described, to thereby drive shaft 5 throughdifferential gear D63 as called for by the slope input D6. The positionor rate of shaft 5 is varied by the curvature input D7 acting throughthe digital-to-analog converter 6% and servo motor 65, differential gearD64, shaft 66, ball slide 67 to integrate the feed rate PR8 and providea shaft output So which is added through differential gear D8? to theshaft 5. Also, the curvature shaft output S6 is modified in accordancewith the rate of curvature change instruction in the input D8 throughthe addition of the shaft output S7, from variable gear ratio V62,through differential gear D64, to shaft 66 and the input of ball slide67 to the integrator BDCfi. The input D8 controls the digital-to-analogconverter 69 which controls the variable gear ratio VG2 having the feedrate input PR7.

The servo circuits of motors 63 and as in FIG. 2 are controlled byswitches S8 and Sh, as in FIG. 1, and later described.

The b output of shaft 5 is thus in accordance with the combinedinstructions in the inputs D6, D7 and D3.

Component Solver of FIG. 3

The terms cos 6 cos g5 (X) and sin 0 cos 75 (Y) are solved by thecomponent solver R2 in FIG. 3.

The planetary gear 12 is so mounted that it will rotate about its center13% while being driven by shaft through crank 114-. Gear 12 meshes withring gear 9, its pitch diameter being equal to /2 that of ring gear Pin21 is integral with gear 12, and is located on the pitch line. it drivesthe Scotch yoke 20 having yokes or sliders 16 and 17. Ring gear 9 isitself driven about its axis 23 by pinion '7 acting through gear 8. Thedistance of pin 21 from axis 23 will be referred to as R". t

The component solver R2 is a combination of the following three devices.

(1) As a planetary differential, if the center 2?; of gear 12 is rotatedabout axis 23' by angle a, and if ring gear 9 is rotated about its axis23 by angle 0, then planetary gear 12 will rotate about its own center23 by angle ot-0.

(2) With ring gear 9 fixed, as planetary gear 12 is rotated about itscenter 23 by an angle 5, pin 21 will proceed in a straight line acrossthe diameter of ring gear 9 in such a way that its distance R" from axis23 is proportional to cos It can be seen that with ring gear 9 9 free torotate, this proportionality still holds, with respect to ring gear 9. I(3) As a resolver, if ring gear 9 is rotated about its axis 23' at anangle 0, then pin 21 will cause yokes or sliders 16 and 17 to moveproportionally to R" cos and R" sin 0.

By combining the above three modes, output yokes or sliders 16 and 17can be caused to move proportionally to sin 0 cos g5, and cos 6' cos qs,as follows:

(a) Revolve center 23 about axis 23' through an angle 0+, by turningshaft 115. Shaft 115 is operated by the sum of angle 0 from FIG. 1 and qfrom FIG. 2 via FIG. 4, these values being added in the differentialgear or adder 3 which supplies the sum 9+ as an output for shaft 115.

(b) Rotate ring gear 9 through angle 0, by turning gear 7, angle 0 fromFIG. 1 being an input to gear 7.

(0) By differential action, planetary gear 12 will rotate about itscenter 23 at an angle a0, where o:=0+, namely at an angle 0+0 or angleTherefore, pin 21 will move along a diameter of ring gear 9 proportionalto cos or R"=cos But ring gear 9 has been rotated through angle 6.Therefore, by resolver action, yokes or sliders 16 and 17 move amountsproportional to R sin 0 and R cos 0, or sin 0 cos and cos 0 cos qb,respectively, since R"=cos s.

As above described, the ball slides 27 and 28 are actuated by the slides16 and 17 respectively to integrate the feed rate FR40 and PR5respectively supplied to the respective integrators 13 and 14, wherebythe shafts S11 and S12 are driven at rates corresponding to the X and Ycomponents of the tool path.

Resolver of FIG. 4

As above described, the angle instruction of shaft 5 from FIG. 2 isresolved by resolver R1 and its Scotch yoke slider 70 into a linearmovement proportional to sin e, slider 70 actuating the ball slide 71 ofthe integrator BDC4 which has the feed rate input PR6, to provide ashaft output S13 carrying a feed rate instruction in accordance with theZ component of the tool path.

Tool Radius Computer of FIGS. 5 and 6 The value of R ordinarily changesonly when the cutter is changed on the machine tool so that it is withinthe scope of the invention to provide for the setting of R by manualdisplacement of the pin 72 with respect to the axis of shaft 76. Theembodiment of the invention illustrated includes means whereby the valueof R as well as the value of 0 and o in the computers can beautomatically and continuously varied. Such manual means for varying thevalue of R may take the form of a crank or handle 88 in FIG. 6 foroperating the shaft 89 which operates the coarse potentiometer 78 andthe fine resolver 80 which operate as transmitters for their respectivecoarse potentiometer receiver 79 and Inductosyn fine data element 81.Servomotor 86 drives the coarse element 79 and the screw 90 and screw 90drives the Inductosyn slider 91 until the error signals from the coarseand fine elements 79 and 81 reach a null, as in usual servo practice.

In FIG. 6, pin 72 is on a carriage not shown driven by screw 90. Thefine position data element coupled to this carriage for indication ofthe position of pin 72 is a precision linear position measuringtransformer, generally indicated at 31. This transformer includes ascale member 92 fastened to table 77 and a slider member 91 fastened tothe carriage not shown. The member 92 includes a continuous multipolarwinding in which uniformly spaced conductors are connected in series andpositioned to extend transversely of the relative direction of motion ofthe two transformer members as established by the lead screw 90. Thetransformer member 91 includes two basically similar multipolar windingswhich are, however, positioned to each other in space quadrature of thepole cycle comprising two adjacent conductors on the member 92. Areference source of voltage is shown at 93 for coarse element 79 and at94 for elements 78 and S0. The swingers of elements 79 and 78 areconnected in opposition through the primary winding 95 of a transformerhaving a secondary winding 96 which supplies the coarse error signal tothe switch 97 which also receives the fine error signal in line 98 fromthe element 81. The error currents are controlled by switch 97 as wellknown and are amplified by amplifier 99 and fed to motor 86.

Also, shaft 89 Which adjusts the radial position of pin 72 may beoperated automatically and continuously by an R-data input indicated at1%, FIG. 6, which may for example include means for converting inputdata into a shaft rotation as shown and described in connection with thedigital-to-analog slope converter 60 of FIG. 2.

Referring to FIG. 6, the motor 86 is controlled to drive pin 72 topositions such that the distance between the axis of pin 72 and of shaft76 accurately represents the cutter radius R, and the shaft 76,indicated as an extension of shaft 5 is driven by the inputs todifferential gear DG3 in FIG. 2 to a position such that the angularposition of pin 72 about the axis of shaft 76 accurately represents,with reference to a prime direction, the angle (,5. In like manner, thepin in FIG. 5 is driven to a position such that the distance between theaxis of pin 85 and the axis of shaft 87, here indicated as an extensionof shaft 4 in FIG. 1, corresponds to R cos at, the shaft 87 being drivento a position determined by the inputs to differential gear DGI in FIG.1.

From the value of R and put into the computer of FIG. 6, the correctionA2: is developed, and from the values of R cos and 6 put into thecomputer of FIG. 5, the corrections Ax and Ay are developed, with a highdegree of accuracy and circuits are provided for connecting FIG. 6 toFIG. 8 and for connecting FIG. 5 to FIG. 7 to combine the programmed X,Y and Z values from the inputs D3 to D8 FIGS. 1 and 2 as manifested inrotations of shafts 4 and 5 so that the X, Y and Z machine elements areoperated to position the center of the machine tool with respect to theworkpiece according to the values X |Ax, Y+Ay and Z-l-Az. It will beunderstood that whether the tool radius correction is added orsubtracted depends on whether the relative position of the cutter withrespect to the workpiece and the origin appropriate choice of leadsdetermining whether addition or subtraction is made and shift from oneto the other can be effected by the program advance.

For development of the correction Az, the pin 72 (see FIG. 6) of theScotch yoke device 73 engages two yokes 74 and 75, respectivelyconstrained by bearing rods, not shown, to move perpendicularly to theaxis shaft 76 and to each other. The Scotch yoke device 73 in FIG. 6 andthe similar Scotch yoke device 83 in FIG. 5 are disclosed in the abovementioned S.N. 561,769, see FIG. 3 and is described and claimed indivisional application S.N. 633,900, filed January 14, 1957, by RobertW. Tripp for Tool Radius Correction Computer, now Patent 2,933,244,.April 19, 1960. If when the angle in the program of the part to be cutis zero, the pin 72 and the axis of shaft 76 are spread apart thedistance R, and if the table 77 thereafter rotates through the angle 5,the yokes 74 and 75 will execute simple harmonic motion of amplitude or,that of yoke 74 being R sin 5 and that of yoke 75 being R cos Thedirection of rotation of table 77 may be made to correspond to increasethe values of the angle 0. Because the values Ax, Ay and Az must bedetermined to a high degree of accuracy, which may be of the order of athousandth or a ten thousandths of an inch, the 0 and g5 values for theangular positions of the tables 84 and 77 and the R values for theradial position of pins 85 and 72 must be supplied with accuracies ofthe same order of magnitude, and means are provided to cause thoseelements to assume positions in accordance with the data thus supplied.To this end, the embodiment of FIGS. 5 and 6 includes both coarse andfine data indicating ele ments for indication of the 0, 5 and R valuesactually assumed by the computers, i.e., the angular position of tables34 and 7'7 and the radial positions of pins 85 and 72. Referring to FIG.6, the R value is indicated by the coarse transmitter 78, its coarsereceiver 79 and by the fine transmitter 311 and its fine receiver 81.Referring to FIG. 2, the value of angle is indicated by the coarse dataelement 61 and by the fine data element 623.

The table 77 and its pin 72 are thus caused to assume positions inaccordance with the values and R supplied to the computer of PEG. 6 fromthe basic program sources where digital values of R and are convertedinto analog values by means of the servo mechanisms described.

There have been thus far described the elements of the computer of FIGS.6 and 12 by means of which the yokes 75 and 74 are caused to assumepositions accurately corresponding to R cos g and R sin (p. Thepositions R sin g5 and R cos qs so established are then transformedaccording to the invention into electrical signals for addition bysuitable apparatus, to be described in exemplary form by reference toFIG. 8, to the z program values for the profile to be imparted to theworkpiece by the machine tool being controlled. This transformation iseffected by means of position data elements coupled between the yokes 75and 74 and the frame of the Scotch yoke device 73.

Both coarse and fine elements are required for generation of electricalsignals representative of R sin (1) and R cos in view of the accuracydemanded in machine tool operation, and it may be advantageous to breakdown the electrical data of R sin :1) and R cos into coarse, medium andfine stage FIG. 5 diagrammatically indicates such an embodiment of thecomputer 33 of the invention with 3 such stages for each of the x and ypositions, while FIG. 6 shows computer 73 with 3 such stages for the 2:position. For generation of coarse and medium position data each of theyokes 75 and 74 has associated therewith gear mechanism diagrammaticallyindicated as including a rack 161D and pinion 162 for position R cos 4)and rack 16d and pinion 162 for position R sin 4 generation of angularmotion. This angular motion is coupled to a potentiometer 164 for R cosand 164' for R sin e the tap of which is shifted from one end to theother of the potentiometer winding not more than once for the fulltravel of the yoke to which it is coupled. In this way unambiguousindications of the coarse increment of R sin e, R cos can be generated.

The linear movements of yokes 74 and 75 are broken down into coarse,medium and fine increments of electrical signals, for addition to thecorresponding increments of the X, Y and Z command shaft instructions asfollows. In FIG. 6, the reference source of voltage 116 supplies thepotentiometer 164, the scale winding 117 of Inductosyn 113, the scalewinding 119 of Inductosyn 12th acting as a fine data transmitter, theprimary winding 121 of transformer 122 and the winding 123 of the mediumresolver 124;.

Inductosyn 118 has quadrature slider windings 125 which are mounted onand slide with the yoke 75 to transmit over the line 126 an electricalsignal proportional to R cos The potentiometer 164' transmits the coarsedata component of R sin and this potentiometer as well as mediumresolver 124 are connected by suitable drive to the pinion 162' asindicated. The coarse, medium and fine electrical signals representativeof R sin are present in the output circuits 127, 123 and 129 of thecoarse data element 164', the medium resolver 12d and the fine dataInductosyn 120 respectively. These values of Az are transmitted to thecoarse, medium and fine transmitters 131, 132 and 133 in FIG. 8.

The coarse, medium and fine electrical values of Ax and Ay are computedin FIG. 5 with a computer which is quite similar to that shown in FIG.6, one difference being that in FIG. 6 the computer 75 has an input ofR, While in FIG. 5 the similar computer 83 has an input of R cos 1).This value of R cos 4) is an instruction in the yoke and it appears incoarse increments in the potentiometer 164, the slider 136 of which isdriven by the pinion 162, and this instruction appears as a fineincrement in the quadrature windings 125. Windings constitute a sliderand are fixed to yoke 75 and are movable relatively to the stationarywinding 117 of Inductosyn 118. The error current from potentiometer 164passes over line 137 to the primary 138 of transformer 13? which has asecondary winding 1419 connected to synchro switch 141 which correspondsto switch 97 in FIG. 6. The error current in line 126 from the slider125 is fed to the quadrature windings 142 of Inductosyn 143, acting as afine data receiver and having a stationary winding 14-4 connected toswitch 141. The potentiometer 145 is a coarse receiver for thetransmitter 164 and they are energized by a reference source of voltage146. This reference source of voltage and others shown may be of theorder of 10 kc., although other frequencies may be used. The servo motor147 is coupled to the coarse receiver 145 and to the lead screw 148which drives pin 35 as well as the quadrature windings 1422. Switch 141thus controls servo motor 147 to position pin 85 from the axis of shaft87 by an amount corresponding to R cos The table 54 is controlled byshaft 87 to the angular position 0, and hence the computer, resolver orScotch yoke device 83 resolves these instructions into a position ofyoke 150 corresponding to R cos 0 cos 5 with yoke 151 in a positioncorresponding to R sin 0 cos 5. As explained in connection with FIG. 6,the motion or position of each of the yokes 1511 and 151 is resolvedinto coarse, medium and fine increments. Accordingly, yoke 151) has thecoarse, medium and fine data transmitters 152, 153 and 154 driventhereby which transmit their electrical signals over the lines 155, 156and 157 respectively, the yoke 151 having similar coarse, medium andfine data transmitters driven thereby and indicated at 158, 159 andrespectively, which transmit their signals over the lines 166, 167 and168 respectively. Application SN. 656,692, filed May 2, 1957, nowabandoned, is a division of SN. 608,357 referred to above and describesand claims resolvers in tandem for computing three dimensionalelectrical components of a linear value R, like resolvers of FIGS. 5 and6 as indicated at the bottom of FIG. 12 of the present application.

The data elements above described for computer 33 have a referencesource of voltage 169.

The mechanical arrangement in the case of fine data elements like 81,118 and 121) in FIG. 6, also 143, 154 and 165 in FIG. 5 is such that thewindings of the two members of these Inductosyns, which conveniently lieon plane faces of insulating supports, are supported parallel to eachother and at a close separation. By a process which is the converse ofthat employed In transformer 143, from excitation of the singlecontinuous windings 171i and 171 of Inductosyns 15 1 and 165 with anA.C. voltage from source 169, a suitable frequency for which may be ofthe order of 10 kilocycles, there will be developed in the quadraturewindings 172 and 173 in-phase voltages whose amplitudes are related asthe sine and cosine of the space phase between the two members of eachInductosyn or position measuring transformer within the pole cyclethereof, zero reference for this phase being that in which the voltagein one quadrature winding of each member is zero and the voltage in theother quadrature winding of that member is at a maximum. This isequivalent to saying that the voltages in the quadrature windings like172 and 173, for example, are proportional to the sine and cosine of theangle through which a shaft would turn if geared to the linear motion ofyokes 151) and 151 to make one revolution for travel of these yokesthrough the pole cycle of windings 171D and 171.

For each of transformers 154 and 165 therefore, the two secondaryvoltages so developed constitute electrical signals representative offine increments in the R cos 0 fed through transformer 215 to switch SW2as described above. Also, the medium resolver 216 is a receiver for itstransmitter 197, the coarse and medium elements 212 and 216 being drivenfrom shaft 221 by the 10 to 1 gearing 222, and the coarse and mediumerror signals therefrom being supplied to switch SW2 to controlservomotor 190 and to drive the driven element 195 to a position calledfor by the instruction in the transmitters 198 and 158, 197 and 184,this instruction being R sin cos ;b which is the Y component of 0 and Rcos In a similar way for Z, the coarse potentiometer receiver 217 isprovided for the coarse potentiometer transmitter 131 and the coarsepotentiometer transmitter 164', a source 218 being provided, the coarseerror signal being fed through transformer 219 to switch SW3, asdescribed above. Also, the medium resolver 220 is a receiver for itstransmitter 132, the coarse and medium elements 217 and 228 being drivenfrom shaft 179 by the to l gearing 223, and the coarse and medium errorsignals therefrom being supplied to switch SW3 to control servomotor 181and to drive the driven element 174 to a position called for by theinstruction in the transmitters 164 and 131, 132 and 133, thisinstruction being R sin 4) which is the Z component of and R.

Referring to FIG. 6 if the pole cycle of the linear position measuringtransformers 81, 118 and 120 is the same, as is conventient, thecalibration of the R input data unit 180 should be such that onerevolution of shaft 89 represents a change in R equal to the pole cycleof the transformers 187, 188 and 177. Negative values of R, for thecutting of inside as contrasted with outside profiles, may be realizedby excursions of pin 72 in the opposite direction from the center oftable 77.

Physically, the resolver-type fine data transmitting elements 182, 184and 133, and their associated coarse data elements 193, 198 and 131 andmedium elements 192 and 197 and 132 may conveniently be located at theprogram units D2 to D8 of FIGS. 1 and 2 where the shaft rotationstherefor are directly available.

Program Advance, Supervisory Control 0 Feed Rate, and General OperationIn connection with the binary gear devices VGll in FIG. 1 and VG2 in H6.2, Patent 2,875,390 describes and claims the sequence of operation ofthe binary gear device in relation to the program advance, with transferof the input data on the card to stepping switches (not shown here) andthe transfer of the decoded binary information on the steppers toholding circuits, to make such control available for quick speed change,while releasing the steppers to receive the next data. These features asdescribed and claimed in Patent 2,875,390, include the octal-to-binarytranslator, differential gear ratio, and sequence of operation of thebinary gear device in relation to the program advance. Such features arenot being claimed here, but may be extended to threedimensionaloperation as indicated herein. Referring to Patent 2,875,390, theoctal-to-binary translator is described page 5, lines 3 to 23; also page31, lines 27 to page 33, line 25 under the heading Octal-to-BinaryTranslator. Referring to Patent 2,875,390, the diflerential gear ratioand conversion to shaft speed are described page 5, line 12 to page 6,line 10; also under the heading Diiferential Gear Ratio page 33, line 26to page 34, line 12. Referring to Patent 2,875,390, see the paragraphunder the heading Sequence page 6, lines 11 to 26; the paragraph underheading Program Advance, etc. page 28, lines 10 to 31; and the matterunder the heading Sequence page 34, line 13 to page 38, line 13. Seealso the paragraph under heading Sequence page 43, lines 11 to 23.

As disclosed and claimed in Patent 2,875,390, provision may be made forreversing the input or output of the binary gear ratio VG1 and VG2 inorder to provide both negative and positive values of rate of change ofcurvature and a Read-1n circuit may be provided to Read the punched cardor tape at a relatively slow rate and during times when the previousinformation is being held in the double relays 2 to 2 on clutch coils,which makes it possible to change the information on the clutch coilsvery rapidly and at an accurately chosen time or under accurately chosenconditions. Referring to Patent 2,875,390, the reversal of the input oroutput of the binary gear ratio is described page 38, lines 1 to 13 inconnection with FIG. 14 of that case.

The error signal circuits for motors M1, M2 and $1 in FIG. 1, alsomotors 65 and 63 in FIG. 2, motor M47 in FIG. 5, motor 86 in FIG.6,motors 189 and 190 FIG. 7 and motor 181 FIG. 8 are shown as a singleline, whereas a complete circuit is understood and is well known.

Concerning the general operation, it is assumed that the origin isestablished by, (a) the machine itself in motion, (b) hand cranks on themachine, or (c) with a manual Zero offset control as described andclaimed in Patent 2,875,390, being also disclosed and claimed in S.N.638,722, filed Feb. 7, 1957, for Zero Offset for Machine Control, nowPatent 2,950,427, August 23, 1960.

It has been found unnecessary to stop the feed rate drive during thetime that the slope and curvature servo motors are operating to adjustthe shaft like 0 and p shafts 4 and 5 in accordance with the currentsegment of the input data and accordingly such control is not disclosedherein whereby the feed rate drive PR is maintained in continuousoperation during the time successive bits of slope, curvature and rateof curvature change input data are adding their instructions to the 0and shafts. The switches indicated at S30 for motor 41, at S10 for motorM2 in FIG. 1 and also at S8 for motor 63 and at S9 for motor 65 in FIG.2 each represents a manual or program advance switch which is closed atthe start of adding a new bit of input instruction, each such switchbeing held closed until the error current to its respective motor isnull, and each such switch again being actuated manually or by theprogram advance when the next bit of input data is to be added to theoperation.

Various modifications may be made in the invention without departingfrom the spirit of the following claims.

I claim:

1. An automatic machine tool control system comprising means for drivingdriven elements along orthogonal X, Y and Z axes at feed rates, meansfor varying said feed rates in accordance with signals representative ofthree dimensional input data characteristic of the path of relativemovement of said driven elements, means for supplying said signals, anda tool radius computer responsive to said data supplying means and meanscontrolled thereby for each of said axes for offsetting the path of saiddriven elements by an amount equal to the tool radius.

2. A machine tool control system comprising means supplying signalsrepresentative of three dimensional input data pertinent to a toolposition with reference to X, Y and Z axes, a shaft for each of saidaxes, converters responsive to said input data supplying means forangularly operating said shafts, means for resolving anguiar movement ofsaid shafts into electrical values for drives along said axes, and atool radius computer responsive to said input data supplying means forshifting the electrical values for each of said axes.

3. An automatic machine control system for driving driven elements alonga path with respect to X, Y and Z orthogonal axes, said systemcomprising means supplying signals representative of input data in termsof said path, means for translating said signals into rotary movement ofa shaft for each of said axes, a servo motor for each of said drivenelements, coarse, medium and fine data elements responsive to each ofsaid first mentioned shafts for controlling the corresponding saidmotor, and a tool radius computer responsive to said input datasupplying means for displacing the said coarse, medium and fine dataelements for each of said shafts.

4. The method of numerically controlling a machine

15. A MACHINE CONTROL SYSTEM FOR A ROTATABLE TOOL, SAID SYSTEMCOMPRISING TWO MACHINE ELEMENTS ON MUTUALLY PERPENDICULAR X AND Y AXES,MEANS PROVIDING AN INPUT SIGNAL REPRESENTATIVE OF A VALUE PROPORTIONALTO THE CONTINUOUSLY VARYING SLOPE ANGLE $ BETWEEN ONE OF SAID AXES ANDTHE TANGENT TO THE SURFACE OF A WORKPIECE TO BE MACHINED BY SAID TOOL,SAID INPUT SIGNAL BEING REPRESENTATIVE OF DATA OF A CURVED LOCUS HAVINGCONTINUOUS CHANGE OF SLOPE EXCLUSIVE OF TOOL RADIUS DATA, MEANS FORRESOLVING SAID SIGNAL REPRESENTATIVE OF THE VALUE OF $ INTO CONTROLSPROPORTIONAL TO SIN $ AND COS $, MEANS FOR CONTROLLING THE SPEED OF SAIDMACHINE ELEMENTS IN ACCORDANCE WITH SAID CONTROLS, MEANS PROVIDING ASEPARATE INPUT SIGNAL REPRESENTATIVE OF A VALUE PROPORTIONAL TO THEMAGNITUDE OF A LINEAR VALUE R, MEANS FOR RESOLVING SAID SIGNALS OFVALUES OF R AND $ INTO INCREMENTS OF SAID SPEED CONTROLS RESPECTIVELY,AND MEANS FOR MODIFYING EACH OF SAID SPEED CONTROLS IN ACCORDANCE WITHITS SAID INCREMENT.